For real-time call information, only the user tokens are able to see the call details. After the call ends and the CDR is written, an admin token can use the Real-Time Call History to get the information about the call (https://developer.webex.com/docs/api/v1/reports-detailed-call-history).
One alternative is to have the user authenticate to an Integration which registers a Webhook. When the user places of receives a call, the webhook will be sent to the HTTP server (yours) and you will have access to the call information as it happens.